The Net can be right-clicked on any Fire Fly or Gecko entity to capture the mob. It will then appear in your inventory as an item, and can be right-clicked on the ground to release the mob. Capturing Geckos is important as they can be placed in Gecko Cages.
Like most other equipment with durability, a damaged Net can be repaired to full durability through an Animator. The more that needs to be repaired, the greater the cost of fuel and crystal charge is in the animation process.